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Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule

  • Norman Schofield

This essay shows that, for any non-collegial voting rule, σ, there exists an integer, s(σ), with this property: if the policy space, W, has dimension no greater than s(σ), then there exists a profile of smooth utilities on W, such that the core for σ at this profile is non-empty and ‘structurally stable’ under sufficiently small perturbation. We also show how we may compute s(σ) for an arbitrary rule. This material is based upon work supported by NSF grant SES-84-18296, to the School of Social Sciences, University of California at Irvine. An early draft was written while the author was Sherman Fairchild Distinguished Scholar at the California Institute of Technology. Thanks are due to Kenneth Shepsle, Dick McKelvey and Gary Cox for helpful comments, to Michael Chwe and Shaun Bowler for research assistance, and to Derek Hearl and Ian Budge for permission to make use of unpublished data. Copyright Martinus Nijhoff Publishers 1986

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File URL: http://hdl.handle.net/10.1007/BF00128877
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Article provided by Springer in its journal Public Choice.

Volume (Year): 51 (1986)
Issue (Month): 3 (January)
Pages: 267-284

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Handle: RePEc:kap:pubcho:v:51:y:1986:i:3:p:267-284
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  1. Schofield, Norman, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Wiley Blackwell, vol. 45(3), pages 575-94, October.
  2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  3. Schofield, Norman, 1983. "Generic Instability of Majority Rule," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 695-705, October.
  4. Kenneth Shepsle & Barry Weingast, 1981. "Structure-induced equilibrium and legislative choice," Public Choice, Springer, vol. 37(3), pages 503-519, January.
  5. Cohen, Linda, 1979. "Cyclic sets in multidimensional voting models," Journal of Economic Theory, Elsevier, vol. 20(1), pages 1-12, February.
  6. Matthews, Steven A, 1982. "Local Simple Games in Public Choice Mechanisms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 623-45, October.
  7. Cohen, Linda & Matthews, Steven A., . "Constrained Plott Equilibria, Directional Equilibria, and Global Cycling Sets," Working Papers 178, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Schofield, Norman., . "Social Equilibrium and Cycles on Compact Sets," Working Papers 484, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
  10. Schofield, Norman, 1980. "Generic properties of simple Bergson-Samuelson welfare functions," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 175-192, July.
  11. Mathew McCubbins & Thomas Schwartz, 1985. "The politics of flatland," Public Choice, Springer, vol. 46(1), pages 45-60, January.
  12. Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
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